Two pistons of a hydraulic machine have diameters 20 cm and 2 cm. Find the force exerted on the larger piston when 50 kg wt is placed on the smaller piston. When the smaller piston moves is throught 50 cm, by what distance the other piston moves out ?

Explanation

To solve the problem step by step, we will use the principles of hydraulics and the relationship between force, area, and volume.

### Step 1: Calculate the Areas of the Pistons
First, we need to calculate the areas of both pistons using the formula for the area of a circle, \( A = \frac{\pi}{4} d^2 \).

- **For the smaller piston (diameter = 2 cm):**
\[
A_1 = \frac{\pi}{4} (2 \times 10^{-2})^2 = \frac{\pi}{4} (0.02)^2 = \frac{\pi}{4} (0.0004) = \frac{\pi \times 0.0004}{4} \approx 3.14 \times 10^{-4} \, \text{m}^2
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